Discrete Geometry: Artin Group Seminar - Michael Dougherty

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There is a natural relationship between the symmetric group and the braid group which can be seen through the construction of an arrangement of hyperplanes in complex space. A similar construction can be used for any finite Coxeter group and its corresponding Artin group, although it is a little less easy to see how the hyperplanes are arranged in this setting. The Salvetti complex gives us a (relatively) simple way to introduce a finite cell structure on the complement of the arrangement, easing our computations. In today’s talk we will assume none of the above definitions - awareness of the fundamental group and cell complexes are the only prerequisites.